III.91 Transforms by T. W. Körner: Pages 303 – 304.

Transforms by T. W. Körner. If a is a sequence a0, a1, a2, , we can define an “infinite polynomial” (Ga)(t) to be S¥r=0 artr. We need to worry about in what sense this sum exists. Formally, (Ga)(t)(Gb)(t) = (G(a*b))(t), where the infinite sequence c= a* b is given by ck = a0bk + a1bk-1+ + akb0 . We call this the convolution of a and b.